An evolutionary topology optimization approach with variationally controlled growth

authored by: D.R. Jantos, P. Junker, K. Hackl
Abstract: Previous works of Junker and Hackl (2016) have presented a variational growth approach to topology optimization in which the problem of checkerboarding was suppressed by means of a discontinuous regularization scheme. This approach did not require additional filter techniques and also optimization algorithms were not needed any more. However, growth approaches to topology optimization demand some limitations in order to avoid a global and simultaneous generation of mass. The limitation has been achieved by a rather simple approach with restricted possibilities for controlling. In this contribution, we eliminate this drawback by introducing a Lagrange multiplier to control the total mass within the model space for each iteration step. This enables us to achieve directly controlled growth behavior and even find optimized structures for prescribed structure volumes. Furthermore, a modified growth approach, which we refer to as the Lagrange shift approach, results a numerically stable model that is easy to handle. After the derivation of the approach, we present numerical solutions for different boundary problems that demonstrate the potential of our model.
External Organisation(s): Ruhr-Universität Bochum
The University of Wuppertal
Type: Article
Journal: Computer Methods in Applied Mechanics and Engineering
Volume: 310
Pages: 780-801
No. of pages: 22
ISSN: 0045-7825
Publication date: 01.10.2016
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Mechanics of Materials, Mechanical Engineering, General Physics and Astronomy, Computer Science Applications, Computational Mechanics
Electronic version(s): https://doi.org/10.1016/j.cma.2016.07.022 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{ab93af94d3794706abc9bc14cf82c452,
title = "An evolutionary topology optimization approach with variationally controlled growth",
abstract = "Previous works of Junker and Hackl (2016) have presented a variational growth approach to topology optimization in which the problem of checkerboarding was suppressed by means of a discontinuous regularization scheme. This approach did not require additional filter techniques and also optimization algorithms were not needed any more. However, growth approaches to topology optimization demand some limitations in order to avoid a global and simultaneous generation of mass. The limitation has been achieved by a rather simple approach with restricted possibilities for controlling. In this contribution, we eliminate this drawback by introducing a Lagrange multiplier to control the total mass within the model space for each iteration step. This enables us to achieve directly controlled growth behavior and even find optimized structures for prescribed structure volumes. Furthermore, a modified growth approach, which we refer to as the Lagrange shift approach, results a numerically stable model that is easy to handle. After the derivation of the approach, we present numerical solutions for different boundary problems that demonstrate the potential of our model.",
keywords = "Constraint evolution, Discontinuous Galerkin approach, Growth, Topology optimization, Variational modeling",
author = "D.R. Jantos and P. Junker and K. Hackl",
note = "Publisher Copyright: {\textcopyright} 2016 Elsevier B.V.",
year = "2016",
month = oct,
day = "1",
doi = "10.1016/j.cma.2016.07.022",
language = "English",
volume = "310",
pages = "780--801",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier",
}